I tried using first order in time and 2nd order in space finite difference scheme, even second order in time and space also. But I am unable to formulate a FD scheme with is stable. I am trying to check stability using von-Neumann stability criteria. Could somebody explain how to proceed in this case?

$\begingroup$What size $\Delta t$ and $\Delta x$ are you using? Using FD methods on that equation will require painfully small values to be stable$\endgroup$
– Michael StachowskyMay 3 at 16:51

$\begingroup$I am currently using 1e-4 for both space and time. The length of both space and time is 1. But the problem is I can't prove using von-Neumann stability criteria that the scheme is stable$\endgroup$
– Aakash GuptaMay 3 at 16:52